Axel Brando

Nataša Tagasovska, Firat Ozdemir, Axel Brando

Despite the major progress of deep models as learning machines, uncertainty estimation remains a major challenge. Existing solutions rely on modified loss functions or architectural changes. We propose to compensate for the lack of built-in uncertainty estimates by supplementing any network, retrospectively, with a subsequent vine copula model, in an overall compound we call Vine-Copula Neural Network (VCNN). Through synthetic and real-data experiments, we show that VCNNs could be task (regression/classification) and architecture (recurrent, fully connected) agnostic while providing reliable and better-calibrated uncertainty estimates, comparable to state-of-the-art built-in uncertainty solutions.

Tomàs Garriga, Alejandro Almodóvar, Axel Brando et al.

Individualized treatment selection with continuous actions requires accurate causal response estimation in decision-relevant regions, rather than uniformly over the entire action space. Estimating a global causal response surface and then choosing the treatment that maximizes it can therefore be suboptimal, since standard estimation objectives allocate modeling effort according to the observed treatment distribution rather than the regions that determine the optimal decision. While decision-aware approaches have been studied in unconfounded settings, this problem remains underexplored in proximal causal inference, where proxy variables and bridge functions enable identification under suitable assumptions even in the presence of hidden confounding. Despite recent progress, proximal methods have primarily focused on treatment-effect and potential-outcome estimation rather than treatment selection and optimal decision-making. To bridge this gap, we introduce a policy-targeted weighted bridge loss that emphasizes decision-relevant treatment regions while retaining global stabilization. We prove a regret bound showing that the proposed weighted bridge loss controls treatment-selection regret through a weighted ill-posedness constant. We instantiate the framework in decision-aware variants of several proximal bridge solvers, yielding practical algorithms that alternate between weighted bridge estimation, response-surface projection, policy update, and weight refinement. Empirically, we find that decision-aware weighting reduces regret across several bridge solvers, suggesting improved treatment selection in proximal settings.

R. Teal Witter, Álvaro Parafita, Tomas Garriga et al.

Structural Causal Models (SCM) are a powerful framework for describing complicated dynamics across the natural sciences. A particularly elegant way of interpreting SCMs is do-Shapley, a game-theoretic method of quantifying the average effect of $d$ variables across exponentially many interventions. Like Shapley values, computing do-Shapley values generally requires evaluating exponentially many terms. The foundation of our work is a reformulation of do-Shapley values in terms of the irreducible sets of the underlying SCM. Leveraging this insight, we can exactly compute do-Shapley values in time linear in the number of irreducible sets $r$, which itself can range from $d$ to $2^d$ depending on the graph structure of the SCM. Since $r$ is unknown a priori, we complement the exact algorithm with an estimator that, like general Shapley value estimators, can be run with any query budget. As the query budget approaches $r$, our estimators can produce more accurate estimates than prior methods by several orders of magnitude, and, when the budget reaches $r$, return the Shapley values up to machine precision. Beyond computational speed, we also reduce the identification burden: we prove that non-parametric identifiability of do-Shapley values requires only the identification of interventional effects for the $d$ singleton coalitions, rather than all classes.

Tomàs Garriga, Gerard Sanz, Eduard Serrahima de Cambra et al.

The ability to accurately perform counterfactual inference on time series is crucial for decision-making in fields like finance, healthcare, and marketing, as it allows us to understand the impact of events or treatments on outcomes over time. In this paper, we introduce a new counterfactual inference approach tailored to time series data impacted by market events, which is motivated by an industrial application. Utilizing the abduction-action-prediction procedure and the Structural Causal Model framework, we first adapt methods based on variational autoencoders and adversarial autoencoders, both previously used in counterfactual literature although not in time series settings. Then, we present the Conditional Entropy-Penalized Autoencoder (CEPAE), a novel autoencoder-based approach for counterfactual inference, which employs an entropy penalization loss over the latent space to encourage disentangled data representations. We validate our approach both theoretically and experimentally on synthetic, semi-synthetic, and real-world datasets, showing that CEPAE generally outperforms the other approaches in the evaluated metrics.

Eddie Conti, Alejandro Astruc, Alvaro Parafita et al.

Understanding how information propagates through Transformer models is a key challenge for interpretability. In this work, we study the effects of minimal token perturbations on the embedding space. In our experiments, we analyze the frequency of which tokens yield to minimal shifts, highlighting that rare tokens usually lead to larger shifts. Moreover, we study how perturbations propagate across layers, demonstrating that input information is increasingly intermixed in deeper layers. Our findings validate the common assumption that the first layers of a model can be used as proxies for model explanations. Overall, this work introduces the combination of token perturbations and shifts on the embedding space as a powerful tool for model interpretability.

Eddie Conti, Álvaro Parafita, Axel Brando

Assessing the importance of individual features in Machine Learning is critical to understand the model's decision-making process. While numerous methods exist, the lack of a definitive ground truth for comparison highlights the need for alternative, well-founded measures. This paper introduces a novel post-hoc local feature importance method called Counterfactual Importance Distribution (CID). We generate two sets of positive and negative counterfactuals, model their distributions using Kernel Density Estimation, and rank features based on a distributional dissimilarity measure. This measure, grounded in a rigorous mathematical framework, satisfies key properties required to function as a valid metric. We showcase the effectiveness of our method by comparing with well-established local feature importance explainers. Our method not only offers complementary perspectives to existing approaches, but also improves performance on faithfulness metrics (both for comprehensiveness and sufficiency), resulting in more faithful explanations of the system. These results highlight its potential as a valuable tool for model analysis.

Josu Eguiluz Castañeira, Axel Brando, Migle Laukyte et al.

Artificial intelligence (AI) now permeates critical infrastructures and decision-making systems where failures produce social, economic, and democratic harm. This position paper challenges the entrenched belief that regulation and innovation are opposites. As evidenced by analogies from aviation, pharmaceuticals, and welfare systems and recent cases of synthetic misinformation, bias and unaccountable decision-making, the absence of well-designed regulation has already created immeasurable damage. Regulation, when thoughtful and adaptive, is not a brake on innovation -- it is its foundation. The present position paper examines the EU AI Act as a model of risk-based, responsibility-driven regulation that addresses the Collingridge Dilemma: acting early enough to prevent harm, yet flexibly enough to sustain innovation. Its adaptive mechanisms -- regulatory sandboxes, small and medium enterprises (SMEs) support, real-world testing, fundamental rights impact assessment (FRIA) -- demonstrate how regulation can accelerate responsibly, rather than delay, technological progress. The position paper summarises how governance tools transform perceived burdens into tangible advantages: legal certainty, consumer trust, and ethical competitiveness. Ultimately, the paper reframes progress: innovation and regulation advance together. By embedding transparency, impact assessments, accountability, and AI literacy into design and deployment, the EU framework defines what responsible innovation truly means -- technological ambition disciplined by democratic values and fundamental rights.

Álvaro Parafita, Tomas Garriga, Axel Brando et al.

Among explainability techniques, SHAP stands out as one of the most popular, but often overlooks the causal structure of the problem. In response, do-SHAP employs interventional queries, but its reliance on estimands hinders its practical application. To address this problem, we propose the use of estimand-agnostic approaches, which allow for the estimation of any identifiable query from a single model, making do-SHAP feasible on complex graphs. We also develop a novel algorithm to significantly accelerate its computation at a negligible cost, as well as a method to explain inaccessible Data Generating Processes. We demonstrate the estimation and computational performance of our approach, and validate it on two real-world datasets, highlighting its potential in obtaining reliable explanations.

Lucas Berry, Axel Brando, Wei-Di Chang et al.

Estimating uncertainty in text-to-image diffusion models is challenging because of their large parameter counts (often exceeding 100 million) and operation in complex, high-dimensional spaces with virtually infinite input possibilities. In this paper, we propose Epistemic Mixture of Experts (EMoE), a novel framework for efficiently estimating epistemic uncertainty in diffusion models. EMoE leverages pre-trained networks without requiring additional training, enabling direct uncertainty estimation from a prompt. We leverage a latent space within the diffusion process that captures epistemic uncertainty better than existing methods. Experimental results on the COCO dataset demonstrate EMoE's effectiveness, showing a strong correlation between uncertainty and image quality. Additionally, EMoE identifies under-sampled languages and regions with higher uncertainty, revealing hidden biases in the training set. This capability demonstrates the relevance of EMoE as a tool for addressing fairness and accountability in AI-generated content.

Unai Gurbindo, Axel Brando, Jaume Abella et al.

Enhancing the robustness of object detection systems under adverse weather conditions is crucial for the advancement of autonomous driving technology. This study presents a novel approach leveraging the diffusion model Instruct Pix2Pix to develop prompting methodologies that generate realistic datasets with weather-based augmentations aiming to mitigate the impact of adverse weather on the perception capabilities of state-of-the-art object detection models, including Faster R-CNN and YOLOv10. Experiments were conducted in two environments, in the CARLA simulator where an initial evaluation of the proposed data augmentation was provided, and then on the real-world image data sets BDD100K and ACDC demonstrating the effectiveness of the approach in real environments. The key contributions of this work are twofold: (1) identifying and quantifying the performance gap in object detection models under challenging weather conditions, and (2) demonstrating how tailored data augmentation strategies can significantly enhance the robustness of these models. This research establishes a solid foundation for improving the reliability of perception systems in demanding environmental scenarios, and provides a pathway for future advancements in autonomous driving.

Lucas Berry, Axel Brando, David Meger

Generative diffusion models, notable for their large parameter count (exceeding 100 million) and operation within high-dimensional image spaces, pose significant challenges for traditional uncertainty estimation methods due to computational demands. In this work, we introduce an innovative framework, Diffusion Ensembles for Capturing Uncertainty (DECU), designed for estimating epistemic uncertainty for diffusion models. The DECU framework introduces a novel method that efficiently trains ensembles of conditional diffusion models by incorporating a static set of pre-trained parameters, drastically reducing the computational burden and the number of parameters that require training. Additionally, DECU employs Pairwise-Distance Estimators (PaiDEs) to accurately measure epistemic uncertainty by evaluating the mutual information between model outputs and weights in high-dimensional spaces. The effectiveness of this framework is demonstrated through experiments on the ImageNet dataset, highlighting its capability to capture epistemic uncertainty, specifically in under-sampled image classes.

Axel Brando, Joan Gimeno, Jose A. Rodríguez-Serrano et al.

Quantile Regression (QR) provides a way to approximate a single conditional quantile. To have a more informative description of the conditional distribution, QR can be merged with deep learning techniques to simultaneously estimate multiple quantiles. However, the minimisation of the QR-loss function does not guarantee non-crossing quantiles, which affects the validity of such predictions and introduces a critical issue in certain scenarios. In this article, we propose a generic deep learning algorithm for predicting an arbitrary number of quantiles that ensures the quantile monotonicity constraint up to the machine precision and maintains its modelling performance with respect to alternative models. The presented method is evaluated over several real-world datasets obtaining state-of-the-art results as well as showing that it scales to large-size data sets.

Axel Brando, Jose A. Rodríguez-Serrano, Jordi Vitrià et al.

In regression tasks, aleatoric uncertainty is commonly addressed by considering a parametric distribution of the output variable, which is based on strong assumptions such as symmetry, unimodality or by supposing a restricted shape. These assumptions are too limited in scenarios where complex shapes, strong skews or multiple modes are present. In this paper, we propose a generic deep learning framework that learns an Uncountable Mixture of Asymmetric Laplacians (UMAL), which will allow us to estimate heterogeneous distributions of the output variable and shows its connections to quantile regression. Despite having a fixed number of parameters, the model can be interpreted as an infinite mixture of components, which yields a flexible approximation for heterogeneous distributions. Apart from synthetic cases, we apply this model to room price forecasting and to predict financial operations in personal bank accounts. We demonstrate that UMAL produces proper distributions, which allows us to extract richer insights and to sharpen decision-making.

Axel Brando, Jose A. Rodríguez-Serrano, Mauricio Ciprian et al.

Deep Learning is a consolidated, state-of-the-art Machine Learning tool to fit a function when provided with large data sets of examples. However, in regression tasks, the straightforward application of Deep Learning models provides a point estimate of the target. In addition, the model does not take into account the uncertainty of a prediction. This represents a great limitation for tasks where communicating an erroneous prediction carries a risk. In this paper we tackle a real-world problem of forecasting impending financial expenses and incomings of customers, while displaying predictable monetary amounts on a mobile app. In this context, we investigate if we would obtain an advantage by applying Deep Learning models with a Heteroscedastic model of the variance of a network's output. Experimentally, we achieve a higher accuracy than non-trivial baselines. More importantly, we introduce a mechanism to discard low-confidence predictions, which means that they will not be visible to users. This should help enhance the user experience of our product.